Sorry for the structuring of the question but it popped in my mind so I stated writing the post.
But first a bit off an overview : The grand duchy of Lithuania was a large state in Eastern Europe which was ruled from Lithuania ( if the name didn’t give off, now you know better). Lithuania was also one of the last area to convert to Christianity in Europe, and held it pagan religion (Romuva) until 1387. And lastly the Lithuanian aristocracy was well connected with their counterparts in the kingdom of Poland, being allies against the Teutonic order, the Swedes, the Russians and many others, which eventually lead the both of them to form the commonwealth.
As the title said, why they didn’t took a greater title like a king of an emperor even! Now I know that titles are sometimes arbitrary and like that but I want to know more about history of the title.
One thing to keep in mind is that "Grand Duke" is something of an imperfect translation of the actual title didysis kunigaikstis in Lithuanian, which would be великий князь in Russian (or related variants of "knyaz" or "knez" in other Slavic languages). The title is something more literally translated as "Great Prince", and was the title held by rulers of territories in the Kievan Rus', and it's successor states, of which Lithuania claimed to be one (Muscovy was also ruled at the time by a "Grand Duke", that is, великий князь).
While we're talking about the Grand Duchy of Lithuania, it's worth recalling that in the period previous to full union with the Kingdom of Poland, the official court language in Lithuania was just as likely to be Old Slavonic or Ruthenian as Lithuanian, and as much or more of the territory's population in 1387 would be Slavic speakers and Orthodox Christians as Lithuanian pagans.
So why go with that term over king (which knyaz and it's variations are distantly related to, by the way) or emperor? In short, those other terms were more closely associated with Western European/Latin conventions that mostly stopped at Poland. As mentioned, Mindaugas was in fact crowned King after converting, but after Lithuanian rulers reverted to paganism it made little sense to claim pretensions to a Western Christian title that technically was bestowed by the Pope in Rome.
Similarly, emperor was not a very common term in Europe at the time, especially as it very clearly had connotations to Rome. Western Christians had one single Emperor until 1804, and that was the Holy Roman Emperor, crowned again by the Pope. Orthodox Christians had an Emperor in Constantinople until 1453, and for all of Lithuanian rulers' pretensions to regather Kievan Rus' under one knyaz, they weren't claiming to be the Third Rome - the Knyaz in Moscow would do that when assuming the title of tsar in 1547 (Peter the Great, that Westernizer, would just change the title to Emperor in 1721).